All biological entities undergoing metabolism consume nutrients and produce waste products to maintain their metabolic processes. Biological entities include organelles, cells, tissues, organs, and organisms. In most instances, exchange of nutrients and waste products occurs continuously between biological entities and an external environment of the entities. For most biological systems, exchange of nutrients and wastes takes place through a particular aqueous medium, such as cytoplasm, intercellular fluid, plasma, lymph, cell-culture media, fresh water, seawater, or blood. Exchange of nutrients and wastes also takes place across structural forms, such as intra-cellular membranes, cell membranes, cell walls, extra-cellular matrix material, alveoli, and capillaries. The rate of exchange of nutrients and wastes is influenced by the particular type of biological entity, the degree of activity of the entity, the composition of the aqueous media and structural forms, as well as the composition of the nutrient or waste material. The nutrients and waste products of most interest with respect to the present invention are the respiratory gases oxygen and carbon dioxide. Exchange of these gases between a metabolically active site of a biological entity and an external environment of the entity is referred to herein as respiration. Respiration of gaseous mass occurs through diffusional means and convective means. The rate of respiration of a particular biological entity is related to the rate of metabolism of the entity.
Metabolism is "the sum of all the physical and chemical processes by which living organized substance is produced and maintained, and also the transformation by which energy is made available for the uses of an organism" (Dorland's Illustrated Medical Dictionary, 27.sup.th Edition, 1988). In the aerobic metabolism of most human cells, for example, oxygen is consumed and carbon dioxide is produced during generation of such high-energy molecules as adenosine 5'-triphosphate (ATP) by catabolism of the nutrient glucose and other metabolic fuels. In this and other metabolic processes, a localized imbalance of nutrients and wastes occurs with respect to the biological entity and an external environment of the entity. If allowed to persist or increase beyond a certain point, the imbalance leads to a life-threatening buildup of wastes or depletion of nutrients. Metabolic processes can be maintained only if nutrients and wastes are exchanged in an appropriate amount and at an appropriate rate.
Diffusion is a means by which gaseous mass is exchanged between a metabolically active site and an external environmental site. Diffusion is driven by a difference in partial as pressure between the sites. As metabolism depletes oxygen at a metabolically active site, for example, a localized "oxygen sink" is established. If an external environment of the biological entity has oxygen at a higher partial gas pressure than the metabolically active site, oxygen is transferred to the metabolically active site through various media and structures by diffusion. Gaseous wastes, such as carbon dioxide, diffuse according to the same process, but in the opposite direction. Diffusion is most effective in biological entities over small distances ranging from inter-molecular distances to a few millimeters.
In discussing animal physiology, Schmidt-Nielsen, (Animal Physiology: Adaptation and Environment, Cambridge University Press, 4.sup.th Edition, pages 16-17 (1990)) employed the following equation developed by E. Newton Harvey (1928) to illustrate that dependence on diffusion alone places distinct limitations on the maximum size to which a population of cells or an organism can grow. This in turn gives an indication of the distances over which diffusion through aqueous media can effectively operate in biological systems as a means of respiratory gas exchange. ##EQU1##
In the equation, F.sub.02 represents the concentration of oxygen at the surface of a spherical organism, expressed in fractions of an atmosphere; V.sub.02 represents the rate of oxygen consumption by the organism as cubic centimeters of oxygen per cubic centimeter of tissue per minute; r is the radius of the spherical cell or organism in centimeters; and K is the diffusion constant in square centimeters per atmosphere of oxygen that will diffuse per minute through an area of one square centimeter when the gradient is one atmosphere per centimeter.
When numbers are used in the equation for a hypothetical organism having a spherical shape and a radius of one centimeter, with an oxygen consumption of 0.001 milliliters per gram oxygen per minute, and a diffusion constant of 11.times.10.sup.-6 per square centimeter per atmosphere per minute (Ibid.), it is found that the concentration of oxygen at the surface, necessary to supply the entire organism by diffusion alone, is fifteen atmospheres. Since the partial pressure of oxygen in the earth's atmosphere and upper levels of the oceans is about 0.21 atmospheres, an organism of this type is too large to exist using diffusion alone. For a more realistic organism having a radius of about one millimeter, the required oxygen concentration at the surface of the organism is 0.15 atmospheres. Well-aerated water at sea level contains about 0.21 atmospheres of oxygen. Accordingly, an organism with a radius on the order of one millimeter could survive on aqueously dissolved oxygen by diffusion alone. Generally, the reliance of these organisms on diffusion through aqueous media to exchange dissolved respiratory gases places a size limit on the organisms of about a one millimeter radius. Viewed another way, diffusion-based exchange of respiratory gases through aqueous media can support the metabolic activity of this hypothetical biological entity only if the diffusion distances required for the exchange of the respiratory gases do not exceed about one millimeter in length. This maximum distance for diffusion-based exchange of respiratory gases between a biological entity and an external environment defines a "diffusion-delimited boundary."
Respiratory gas exchange within a diffusion-delimited boundary is referred to herein as occurring within an "internal respiratory system." Examples of biological entities that function within an internal respiratory system include mitochondria, chloroplasts, individual cells, single-celled organisms, small multi-cellular organisms, collections of small numbers of cells, and specific anatomic regions of certain aquatic organisms, such as jellyfish. Depending on their actual size and metabolic requirements, the cell walls, cell membranes, or the edges of the cell masses usually represent the diffusion-delimited boundary of these biological entities. These entities survive within a diffusion-delimited boundary because diffusion-based exchange of respiratory gas occurs over distances that are effective in transferring respiratory gases in sufficient amounts and at sufficient rates to support the metabolic activities of the entities.
In many cases, the diffusion-based process of the internal respiratory system may be supplemented by convection-based processes beyond the diffusion-delimited boundary. Respiratory gas exchange beyond a diffusion-delimited boundary is referred to herein as occurring in an "external respiratory system." Gas exchange in external respiratory systems occurs with the aid of convection-based means. Examples of convection-based external respiratory systems include animal vascular systems and pulmonary systems of both aquatic and terrestrial organisms. External respiratory systems are characterized by well defined anatomical structures that maintain convection-based processes in an organism. In contrast to passive diffusion-based internal respiratory systems, all external respiratory systems rely on energy expenditure to function.
Insects represent a solution to respiratory gas exchange that enables diffusion-delimited boundaries to exceed those of organisms restricted to diffusion-based exchange of respiratory gas through aqueous media alone. As Schmidt-Nielsen teaches (Ibid., p. 17):
Insects have a special form of respiratory system. Small openings on an insect's body surface connect to a system of tubes (tracheae) that branch and lead to all parts of the body. In this case the respiratory organ combines a distribution system (the tubes) with the gas-exchange system, for most of the gas passes through the walls of the finest branches of this system and diffuses directly to the cells.
A generalized illustration of an insect tracheal system is shown in FIGS. 1A and 1B. In an insect respiratory system, large air-filled structures, called "tracheae," provide directed transport of respiratory gases to and from an external environment. Gases are conducted within the insect body through increasingly smaller, yet more numerous, air-filled "tracheoles." Beyond the tracheoles are "tracheole termini" where the gases diffuse across the tracheole walls to metabolically active sites. It is noteworthy that the gas-exchange system in an insect is separate from the liquid-exchange system. Insects do not rely on liquids, such as blood, to collect, transfer, and distribute respiratory gases to and from tissues in the animal. Rather, they use the tracheal system. Air in the insect respiratory system is an excellent medium for rapid and directed exchange of respiratory gases between an external environment and metabolic sites deep within the insect's body. This is primarily due to much lower resistances presented to a diffusing gas by a gaseous medium than resistances presented to respiratory gases diffusing through water or an aqueous media.
An open tracheal system (e.g., FIG. 1A) may or may not combine convection-based gas transport processes with diffusion-based processes as a means of exchanging respiratory gases between an external environment and metabolically active sites in an insect. In these systems, convection-based exchange of respiratory gases may occur through trachea in fluid communication with an external environment. The diffusion-based exchange of respiratory gases occurs at the level of the tracheoles or tracheole termini. The boundary between the convection-based processes and the diffusion-based processes may be dynamic, changing with the respiratory rate and physical movement of the animal, for example. Accordingly, convection-based exchange of respiratory gases may not be present at all, as in the case of a goat moth larvae, or convection-based exchange of respiratory gases may represent a significant portion of exchange in insects, such as an active bumble bee.
FIG. 1B illustrates an insect with gas-filled respiratory structures that are closed to the environment outside the insect by a gas-permeable membrane sealing the openings to the trachea. Respiratory gas exchange occurs in this insect type entirely by diffusion without the aid of convection-based means. Accordingly, the entire tracheal system of these insects represents a particular example of an anatomical structure that functions as an aid to internal respiration. This system is successful in these insects because diffusion-based exchange of respiratory gases through air-filled void spaces is an energy efficient means of moving relatively large amounts of respiratory gases to and from metabolically active sites across distances much larger than those possible through water or aqueous media alone. This type of diffusion-based exchange of respiratory gases through discrete gas-filled spaces is central to the present invention.
The efficient collection, conduction, and distribution of respiratory gases through air-filled conduits in insects is largely determined by the geometry of the respiratory structures. Particularly elegant respiratory structures are ones having a ramiform geometry. Such structures are replete in nature (FIG. 2).
Modifications of insect respiratory systems that enhance collection of respiratory gases include structures commonly referred to as "gills." Gills are specialized gas-collecting structures having high surface area-to-volume ratios that are conjoined with numerous highly divided tracheoles in close apposition with the gill surfaces. The high surface area-to-volume ratios enable the gas-collecting structures to serve as a means of improving gas transfer through layers of water that are resistant to diffusion of gas. Stagnant layers of water reside at the immediate boundary between the outer surfaces of these gas-collecting structures and an external aqueous environment.
Tracheoles have properties that permit respiratory gases to be efficiently conducted through structures having very small cross-sectional areas. As the diameter of insect tracheoles is decreased, the number of tracheoles occupying the same volume can be increased. Increased numbers of tracheoles permit ramification throughout the insect's body, thereby providing respiratory structures in close proximity to metabolically active sites in the insect's body. A decreased diameter in the tracheoles also means the surface-area-to-volume ratio of individual tracheoles increase. As the surface-area-to-volume ratio is increased, the number of cells that can be supported increases. The net result is that insect respiratory structures provide efficient collection, conduction, and distribution of respiratory gases from the environment to metabolic sites deep within the insect.
Artificial biological systems, such as cells contained within a cell-containing device, also undergo respiration. Artificial biological systems exchange nutrients and wastes by diffusion-based means. In many applications, convection-based means are employed to assist respiratory gas exchange in cell-containing devices. As with cells in natural diffusion-delimited systems, there are limits to the size and shape that a cell mass can assume in a diffusion-based cell-containing device. A common feature of most cell-encapsulation devices is a permeable membrane that serves to retain a population of cells within the device, while allowing nutrients and wastes to passively exchange across the membrane in support of the metabolic activity of the encapsulated cells. The exchange of nutrients and wastes occurs through aqueous liquid-filled channels established in the membrane during use. Cells within the device cannot be positioned farther from the permeable membrane than diffusion of nutrients and wastes can support. The permeable membrane may represent a diffusion-delimited boundary in cell-containing devices. As can be deduced from the Harvey Equation and examples from nature, a metabolically active cell in a cell-containing device cannot thrive if positioned more than a few hundred microns from a permeable membrane through which nutrients are supplied if the cell is to be supported by diffusion across the membrane through aqueous media alone.
In addition to the constraints imposed on a population of encapsulated cells by the limited mass-transport capacities of aqueous-mediated diffusion, the permeable membrane presents further limitations on the size, shape, and performance of a contained cell mass. A principle limitation to the diffusion of respiratory gases across a permeable membrane in a cell-encapsulation device is the need to use aqueous channels traversing the membrane as media through which the gases are transported across the membrane. Aqueous channels present a limitation to respiratory gas transport because most aqueous media are not particularly good substances for dissolving and transporting respiratory gases. This is the case both in terms of the concentrations of gases that can be dissolved in the aqueous media, as well as the rates of movement of the gases through the aqueous media. As a result, the use of aqueous channels as a means to support exchange of respiratory gases in a cell-encapsulation device is inadequate for cell masses more than a few hundred microns in thickness or more than a few hundred microns removed from a diffusion-delimited boundary.
As with natural systems, cell-encapsulation devices have internal respiratory systems. Some cell-encapsulation devices are designed to incorporate external respiratory systems. Encapsulated cell masses more than a few hundred microns in thickness or more than a few hundred microns removed from a diffusion-delimited boundary usually require an external respiratory system to supplement the processes of diffusion operating in the internal respiratory system. With implantable cell-encapsulation devices, for example, an external respiratory system in the form of implant host capillaries is often induced to grow close to the device (Hunter, et al., "Promotion of neovascularization around hollow fiber bioartificial organs using biologically active substances," ASAIO Journal, Vol. 45, pp.37-40, (1999)). A close association of capillaries with a permeable cell-encapsulating membrane is said to result in an increase in the concentration gradient of oxygen on an external surface of the permeable membrane. Another strategy to establish an external respiratory system in association with a cell-encapsulation device is the use of well-perfused tissues as in-vivo implantation sites (Dionne, et al., "Effects of oxygen on isolated pancreatic tissue," Transactions of the American Society for Artificial Internal Organs, Vol. 35, pp. 735-741 (1984)). Finally, in an extreme case, some investigators have placed cell-encapsulation devices in direct contact with an external respiratory system in the form of flowing arterial blood (e.g., Monaco, et al., "Transplantation of islet allografts and xenografts in totally pancreatectomized diabetic dogs using the hybrid artificial pancreas," Annals of Surgery, Vol. 214, pp. 339-362 (1991)). This technique is usually impractical as it carries a risk of thrombosis and embolism to the implant recipient. All these manipulations of external respiratory systems to enhance oxygen concentrations at the external surfaces of cell-containing membranes have only modest effects on enhancing transport of respiratory gases across the cell-containing permeable membranes. This is due primarily to resistances to transport of respiratory gases inherent in permeable cell-containing membranes that rely on aqueous liquid-filled channels as means through which exchange of respiratory gases occurs. Increasing the performance of an external respiratory system cannot remedy mass-transport limitations in artificial biological systems that are the result of a deficient internal respiratory system design.
With these and other artificial biological systems, materials that improve passive mass transfer of respiratory gases to and from metabolically active sites within the systems would be advantageous. The materials would aid the internal respiration of these artificial biological systems by collecting, conducting, and distributing respiratory gases between a diffusion-delimited boundary of the artificial system and metabolically active sites within the system. The materials would permit cell populations contained within diffusion-based devices to be greater in thickness than a few hundred microns. The materials would also allow cells in diffusion-based devices to be located more than a few hundred microns from their diffusion-delimited boundary. The materials would also provide for greater respiratory gas exchange, and thus greater cellular activity and performance.